I heard about TweetDeck many times as a way to manage your twitter account. It is an application you download to easily and efficiently manage your twitter account. I am glad I finally tried it and was very impressed.
The interface can be arranged in many ways, a common way is the image below. You can see 3 columns, one with all the tweets of everyone you are following (labeled as #1), one with the replies to you (labeled #2), and the third column has tweets sent only to you known as the direct messages (labeled #3).
You can also reply to tweets in the top row (labeled as #4). When you view an individuals profile it also pops up into the application. You can completely manage your twitter account without ever visiting the Twitter website nor having to tab back and forth between replies, direct messages etc.
TweetDeck works on Mac OS and Windows machines. It is free, however you may donate. Find TweetDeck here .